Math

posted by .

1a) Prove that there exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2

1b) use similar idea to prove that there exists a rational number a and an irrational number b so that a^b is irrational

1c) prove that if 2^√2is irrational then √2^√2is irrational.


Thanks for your help.

  • Math -

    (√2^√2)^√2 = √2^(√2*√2) = √2^2 = 2

    √2^√2 = (2^1/2)^√2 = 2^(1/√2)

    That should get you started

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math

    Find an equation of the line that bisects the obtuse angles formed by the lines with equations 3x-y=1 and x+y=-2. a. (3√2 +√10)x-(√10 + √2)y-2√10+√2=0 b. (3√2 - √10)x+(√10 - √2)y+2√10+√2=0 …
  2. irrational numbers?!

    what are rational and irrational numbers?
  3. algebra/trig

    1. which number below is irrational? a)√4/9 b) √20 c)√121 Why is the number you chose irrational?
  4. Algebra

    Order the following numbers from least to greatest. √5, -0.1, (-5/3), 0.7, √2 a. 0.7, √2, (-5/3), √5, -0.1 b. √5, √2, 0.7, (-5/3), -0.1 c. (-5/3), -0.1, 0.7, √2, √5 ?
  5. please help with math

    There exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2 a) use similar idea to prove that there exists a rational number a and an irrational number b so …
  6. THE HOMEWORK IS DUE TODAY- HELP! HELP! PLEASE

    There exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2 a) use similar idea to prove that there exists a rational number a and an irrational number b so …
  7. math

    There exist irrational numbers a and b so that a^b is rational. look at the numbers √2^√2 and (√2^√2)^√2 a) use similar idea to prove that there exists a rational number a and an irrational number b so …
  8. 8th grade algebra

    Can you check my answers? 1. 3√20/√4 = 3√(5)(4)/2 = 3(2)√5/2 = 3√5 2. 4√15/√9 = 4√15/3 3. √12/√16 = √4(3)/4 = 2√3/4 = √3/2 4. √10/√5 = √2
  9. Algebra

    1. Simplify the expression: 4√18+5√32 A.45√2 B.32√2 C.116√2 D.9√50 2. Simplify the expression: 7√5-3√80 A.-5√5 B.-4√75 C.-5 D.4√-75 3. Simplify the expression: √21(√3+√14) …
  10. Algebra - Check My Work

    For Question 1-8 Simplify the Radical Expression *** - My Answer 1.√45 3√5*** 2.√180x^2 6x√5*** 3.√150x^3 k^4 5xk^2√6x*** 4.√21y * 5√49y 35y√21*** 5.(The square root sign applies …

More Similar Questions